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Treebeard's Stumper Answer
10 March 2000

Strange Views

Part of the challenge of technical drawing or drafting is learning to show solid objects in flat drawings. A common method is to use orthographic projections to show the edges of an object with front, top, and side views. Here's an example, and two stumpers. The puzzle is to study the three views and reconstruct the solid objects they show. All surfaces are flat, though not necessarily at right angles to each other. There are no hidden edges. Hint: each object can be carved from a solid block with just one or two straight cuts!


Four Dunn Middle School students were the first to independently find both stumper blocks shown below. This requires real visual thinking! The first object is made with two straight cuts, one diagonally across the top and straight down, the other diagonally across the side and in until they meet. The other object can be made with a single cut from the top diagonal down at an angle to the front corner. It's not surprising that much drafting is now done on computers with CAD software that lets the designer manipulate solid objects in virtual 3D space.

Notes:

Graybear did me one better and produced developments of each object showing how they can be made from a piece of paper. If each square is 1 by 1, then how long are the diagonals? (Hint: c2 = a2 + b2)

Challenge accepted, Graybear! I cut and pasted your developments into a graphics program, enlarged them and added glue tabs, printed them on heavy paper with my ink jet printer, and made them. Nice fit!

My plans are available here and here. Save the images and load them into a graphics program like Paint Shop Pro. Print them full page in landscape mode on card stock or photo paper. Crease all the folds (scoring will help) and paste them together with a glue stick. Let the ink dry a long time before folding so they won't be as smudged as mine! This is a handy way to make paper model templates for a drafting class. Now there's an idea for a useful Web site!

I didn't think I'd have anything to say about this stumper, but I was wrong. I presented this stumper in each of my science classes at Dunn Middle School, and gave the kids just five minutes to do it. Four kids (of 48) got both stumpers. What's interesting is that three of the four kids are in special tutoring classes. We all learn in different ways, and this shows that kids who need help with normal school tasks can excel at other important tasks.

I've always been skeptical about left-brain / right-brain dichotomies. That dualism just seems too simple and archaic to be anything more than a metaphor. But it's undeniable that we're different, and it's a step in the right direction for teachers.

In this election year, it seems politicians can't talk about education without mentioning "standardized testing." That scares me. I don't see the point of trying to make everyone the same. This policy hurts kids, and it will hurt our country in the long run. I want diversity and more opportunities for kids in schools, not narrow standards. Arts and vocational training and other educational alternatives are important. They allow different kids to shine.

Of course that's just my opinion. I may be wrong.

Here are some Web links for further research on visual learning:

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Copyright © 2000 by Marc Kummel / mkummel@rain.org